Determination of melting temperatures in hydrocarbon mixtures by differential scanning calorimetry

Highlights

• A robust technique for determining melting temperatures in hydrocarbon mixtures by DSC has been established.

• Melting temperatures determined via the endset scanning method were found to be consistent with cryoscopic measurements and the stepwise method.

• The impact of any sample de-mixing that may have occurred over multiple freeze-melt cycles was negligible.

• New SLE data for heptane + hexadecane, hexane + hexadecane and hexane + para-xylene + hexadecane.

Abstract

There is a lack of consistency in the literature about how to determine the melting (liquidus) temperature in a hydrocarbon mixture from thermograms recorded by differential scanning calorimetry (DSC). This paper establishes a robust technique for determining liquidus temperatures by DSC by testing two methods detailed in the literature and assessing the potential for de-mixing to preclude repeatable measurements. Liquidus temperatures determined via the end set scanning method were found to be consistent with literature measurements of the same mixture obtained visually, and with a liquidus temperature measured for a fresh sample using the step method. In contrast, use of the thermogram’s peak temperature produced inconsistent results that often could not be reasonably extrapolated to zero scan rate. The impact of any sample de-mixing that may have occurred over multiple freeze-melt cycles was negligible, as demonstrated by the consistency of the thermograms repeated at the same scan rate, and the consistency of liquidus temperatures obtained with different sample loadings into the DSC. New (solid + liquid) equilibrium results are reported for {heptane + hexadecane (C₁₆)} and (hexane + hexadecane) binaries as well as a (hexane + para-xylene + hexadecane) ternary over a temperature range from (260.80 to 279.17) K at atmospheric pressure. Comparisons of the binary measurements against both literature data and the calculations with a property package implemented in commercial software showed deviations of less than 1 K for mixtures with C₁₆ solute mole fractions around 0.3, and −3 K for the mixture with a C₁₆ solute mole fraction around 0.1, due to the increasing sensitivity of the liquidus temperature on composition as the solute fraction decreases. The ternary mixture, with a C₁₆ solute mole fraction of around 0.1, showed a deviation of −5 K, suggesting the property package does not adequately capture the interactions associated with the presence of an aromatic component.

Introduction

Significant capital expenditure and operating costs are involved in the production of liquefied natural gas (LNG). Essentially, following treatment of the natural gas to remove non-hydrocarbon impurities, there are two major steps involved in LNG production: (1) the separation of hydrocarbons heavier than ethane (C₃₊) from the methane-rich mixture, and (2) liquefaction of the methane-rich mixture by cooling to cryogenic temperatures. The effectiveness of step (1) can be reduced, for example, by disturbances in process control, or as a result of poor vapour-liquid equilibrium (VLE) predictions, resulting in higher concentrations of C₃₊ than expected in the methane-rich mixture [1], [2], [3], [4], [5], [6]. Consequently, during the liquefaction step there is a risk of hydrocarbons heavier than butane (C₅₊) freezing out at the cryogenic operating temperatures. These C₅₊ solids can deposit on the inner surface of the processing equipment resulting in reduced heat transfer efficiency or, more severely, blockages. Therefore, models that can predict reliably the risk associated with this deposition are needed.

A model’s effectiveness for predicting this risk of solid formation depends on the thermodynamic framework used to describe the solid-liquid equilibrium (SLE). Most existing models for SLE predictions have frameworks that are based either on empirical activity coefficient models [7] or on approaches based on cubic equations of state (EOS) [8], [9], [10], [11], which can also be used to predict other thermodynamic properties. The models can, in both cases, be anchored to measured SLE data for binary mixtures. However, there is a deficiency of SLE data for binary mixtures composed of the hydrocarbons and at the cryogenic conditions relevant to LNG production. Most data available come from cryoscopic measurements made using visual cells [7], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. However, while cryoscopy has proven effective, it requires manual observation and is often unable to provide information about other thermodynamic properties of interest. Additionally, operating a cryoscopic apparatus at cryogenic temperatures can be subject to substantial complications.

Differential scanning calorimetry (DSC) has the potential to provide an alternate, automated method to measure SLE. This method measures the difference in heat absorbed between a sample and reference when undergoing a temperature increase or decrease, respectively. It is a well-established thermoanalytical technique capable of measuring a wide array of thermodynamic properties including isobaric heat capacity (c_p), molar enthalpy of fusion (Δ_fusH), melting temperatures (T_melting) for pure components and liquidus temperatures (T_liquidus) for mixtures – all of which are required in many SLE models. For clarity, the term liquidus refers to the condition at which the last solid crystal melts into a bulk liquid phase, while the term solidus refers to the formation of a first liquid droplet in equilibrium with a bulk solid phase. Fig. 1 shows schematic examples of typical thermograms observed when a pure hydrocarbon undergoes a solid-liquid phase change (Fig. 1(a)) and when as a single phase liquid it undergoes a temperature change (Fig. 1(c)). The measured heat absorbed in both thermograms is determined by integration of the heat flow curve with time. From the total heat absorbed and the known sample mass either the enthalpy of fusion (Fig. 1(a)) or, when combined with the measured temperature change, the isobaric heat capacity (Fig. 1(c)) can be calculated. It is worth noting that in both cases the associated temperature scans (Fig. 1(b) and (d)) are qualitatively similar even though the measurement in Fig. 1(a) is probing a property that occurs at a fixed point, while the measurement in Fig. 1(c) probes a property associated with a temperature interval.

To determine the melting temperature, T_melting, from Fig. 1(a) the characteristic onset temperature of the thermal peak is first identified using the method shown in Fig. 2. The onset temperature is determined from the intersection between the tangent to the maximum rising slope upon melting, and the sample baseline curve measured prior to any melting [27]. Heating curves are used exclusively to determine T_melting because of the subcooling frequently observed with solidification. Onset temperatures are determined from several thermograms measured using multiple scan rates slow enough to minimize temperature gradients within the sample during the temperature change, while still producing a significant signal-to-noise ratio. A linear relationship between the onset temperature and scan rate is generally observed, which enables T_melting for a pure fluid to be determined from the onset temperatures by extrapolating them to a zero scan rate; this procedure mitigates the thermal lag effect inherent to the DSC method [28].

In principle, DSC can be applied to the determination of T_liquidus in hydrocarbon mixtures exhibiting eutectic behaviour but there are some key differences from pure fluids, which cause challenges that may have prevented its wider adoption. The two main challenges are (1) potential de-mixing of the sample due to stratification upon melting, and (2) interpretation of the thermogram produced during the melting process, because the onset of the thermal peak is smeared due to the dependence of T_liquidus on composition. The objective of this work is to show, for certain mixtures, how these challenges can be overcome. Studies of melting in hydrocarbon binary mixtures using DSC exist in the literature [30], [31], [32], and while none to our knowledge explicitly address the potential problem of de-mixing, their publication suggests that this first challenge might be mitigated sufficiently through the convective mixing that occurs in a cell due to the temperature scanning central to the method. In this work, we use the repeatability of our measurements and their consistency with literature SLE data measured visually to assess whether challenge (1) is in fact a significant issue for the types of systems studied here.

The literature is not consistent regarding how challenge (2) should be dealt with. The application of DSC to the study of organic mixtures has seen a number of methods developed to determine T_liquidus from the thermogram observed during the melting of the solid phase. Some studies identified T_liquidus from the onset temperature despite the qualitatively different nature of melting in a mixture to that in a pure substance (i.e. melting at constant pressure occurs over a range of temperatures in systems where the liquid phase composition varies as the solid phase melts) [33]. Other studies have identified T_liquidus as the temperature corresponding to the turning point of the thermal peak, which is characterised as the peak temperature [34], [35], [36], [37], [38], [39], [40]. However, it has been shown that this peak represents the point where the energy exchange between the sample and thermopiles is at a maximum and does not correspond to the point of complete dissolution [30]. Some studies have adopted numerical procedures applied[41], [42], [43], [44], [45] post-experiment that take into account factors influencing the shape of the thermogram to identify T_liquidus from the data [41], [42], [43], [44], [45]. These procedures treat the DSC as a black box with a transfer function relating an imaginary DSC curve, calculated using phase equilibrium and the solid fraction formed, to the measured DSC curve. The transfer function is derived from a pure component thermogram, which is often approximated by a triangle-type representation. Additionally, the solid fraction must be calculated, usually via the lever rule. Thus, these methods are limited by their reliance on the accuracy of the thermodynamic models employed, the calculation of the solid fraction formed, and the transfer function description of the factors influencing the thermogram shape.

In this work, we demonstrate the use of the end set temperature as a robust and straightforward means of identifying T_liquidus in hydrocarbon mixtures; determination of the end set temperature is shown in Fig. 3 and is analogous to that used to determine the onset temperature in pure substances (but in the opposite direction). Smith and Pennings [46] proposed and employed the end set temperature extrapolated to zero scan rate [46]. However, other studies that have adopted this approach used a single scan rate slow enough to be considered a good approximation [47], [48]. Kousksou et al. investigated melting in hydrocarbon mixtures with DSC both experimentally and numerically [30], [32]. The numerical model was used to give physical meaning to the experimental thermogram and identified T_liquidus as the extrapolated end set temperature. Here we present a method of determining the end set temperature for a given DSC thermogram without reference to a numerical model, and then extrapolate these measured end set temperatures to zero scan rate to obtain T_liquidus. The results of this scanning DSC method are validated by comparison with static (non-scanned) DSC measurements as well as with SLE data and models in the literature.

Ambient pressure (≈101 kPa) SLE data are presented in this work for three pure substances (to establish the standard uncertainty of the temperature and heat flux measurements over the range 175 K to 283 K), four binary mixtures and a ternary mixture. Literature SLE data exist for only two of the binary mixtures; for the two other mixtures, comparisons are made with the predictions of cubic EOS which have been anchored to VLE data. The results presented here establish a domain of applicability for mixture T_liquidus measurements with the DSC method, which will be applied in the future to the study of SLE in high pressure systems of more relevance to LNG production.